Kinkyhairlady your question is really hard to answer, because breakage comes in many forms. Breakage from mid-strand splits or happening further up the strand like at the point of demarcation in relaxed hair or because of trauma from a clip cannot be helped by trimming.
Breaking-off ends due to splits or normal wear and tear can be PREVENTED if caught before the damage has happened. Otherwise any cut or trim after the fact is simply to get rid of the damage rather than waiting for the hair to break off on its own. The positive thing about cutting it off instead of letting it fall off on its own is you can create a neat (tougher) end, rather than risk a new rugged end that continues splitting repeating the same problem you just had.
Those^^ ends will continue breaking off because each torn-off part of a strand is weaker than the whole so whether you cut them off or not, they will break off over time, just because they cannot hold moisture, or withstand manipulation. Cutting them above where the fray has occurred would leave you with a stronger strand because it's whole and has no fray. Cutting with sharp scissors would ensure the end is smooth and has no notches for easy splitting. As I explained in
this post, keeping notches at bay are the reason some of us find regular dusting helps us retain better. When we don't dust, the cycle I explained above takes place which is why some of us stay at SL for all our lives.
And if you've managed to get away w/o dusting and are now at APL or beyond but finding breakage a problem, it's because the ends are now many years old. Organic things do wear and tear, so just because you made it this far, doesn't mean the same cycle many deal with can't catch up with you. Of course, there's the abnormal handful who can just do whatever and still sit on their hair. But if that's not you, then regular dusting might be for you.