Define "overworked" as you are being paid for your time & competence in completing work as assigned. If you are not doing the job well enough to keep up, don't expect to keep the job. If you expect time to fiddle around, socialize, etc, between breaks, you need to look for another job. If you are working flat-out, highly effective & efficient, & it is simply impossible to get all the work done, then it is time to talk to your superior about getting additional staff.
Think about an assembly line, and turning it up faster-faster-faster until even the best worker cannot do the job. That's ridiculous. That's when unions go on strike, not before.
It's not that management "doesn't care." Everybody is under pressure to do better, do more with less, and get the best & most competent people on the job. Every person has to produce enough to justify their costs, and competition is very tough these days.