I would argue that there are a few ways this phrase can be inverted:
No rights reserved
Implies that the author waives all rights to his/her work (i.e. ultimately places it in the public domain)
All rights included
I've seen this one in the context of royalty-free music being used in the commercial sense, where if you pay for the license, you can use that song anytime anywhere, with all rights to the song. This seems to be the opposite of "All rights reserved" which we should know by now what it means
Copyleft
While not really a phrase, it is the opposite of copyright itself. Used primarily in software but maybe some other media can also be considered copyleft. As far as I'm aware, it has some ties with copyright itself (that you cannot remove attribution from the author, and, in case of software, must distribute it as is, without putting any restrictions yourself)
There are probably more means other than what I've listed, and I would love to hear your thoughts and suggestions!
The idea of copyleft is that you give anyone the freedom to do anything with your work, with one essential restriction: they do the same for their changes, derivative works etc. Technically attribution doesn't have to be part of a copyleft licence, but all copyleft licences I know have a requirement to preserve copyright info.
And yes, it is popular in software (GPL, MPL, EPL), but for other types of works there is CC BY-SA 4.0 (Creative Commons Attribution-ShareAlike). If you want to copyleft books, images, videos, other forms of text... this is the way to go, IMO.
Some additional remarks, just to clarify:
Copyleft is not "giving up all copyright" - copyleft essentially "plays" the copyright system in a way that makes sure nobody is restricting access to or usage of one's work. Using the rules of copyright against copyright, if you will.
In some jurisdictions, there is no such thing as "giving up all copyright" or "dedicating something to the public domain". Best you can do, generally, is giving users all the same/relevant rights.
Most Creative Commons licences are not copyleft, only the ones with a ShareAlike (SA) clause. Some CC licences are also nonfree, meaning they don't give you all the freedoms to do what you want with the work. The 2 possible nonfree clauses in CC licences are ND (no derivative works) and NC (no commercial use). NC can also be used together with a SA clause, making CC BY-SA (free) and CC BY-NC-SA (nonfree) the two CC copyleft licences.
I recently made a Jamendo account myself, and I already found an album to download ("Show it to your Mother" by Rusty Tea Makers). I find it easier to find music there than on FMA
Weird/confusing name, questionable legality and the website went down a while back (while mentioned explicitly in the licence...)
Use CC0 1.0 or Zero Clause BSD instead. They are more reputable, and all decent "public domain equivalent" licences are... well, equivalent in effect, anyway.
afaik some people are worried about the "legal enforceability" of the unlicense, which is funny given the point of it is to be an explicit "go do what you want" license.
You've just stepped into a minefield. Look up the difference between the MIT and GPL licences. If you're into that sort of thing it can be fascinating, but basically it boils down to two camps:
Your license preserves your freedoms by binding the licensee to a guarantee that they'll preserve your freedom.
Your license preserves nothing, but guarantees the licensee the right to do anything they want.
Each camp claims theirs is "more free". Only one can be right.
I'd like to disrespectfully disagree, it's a trainwreck of a license and while I get the memeing, some people actually go ahead and use it seriously, just because they can't be bothered to put some thought into how their software should be treated, that doesn't protect neither themselves nor the users
I had the same question dozen years ago when was taking part in publishing one book (in my translation from French). Publishing house finally used phrase which in English should sound like: "Not protected by copyright law".