My headphones broke at worst place possible

@alfiaali you are right. That is pretty much one of the worst places since no adhesive will work on anything that is supposed to move/swivel. You could try to use some two epoxy adhesive and not try to readhere the broken part but to disable it completely. Apply the epoxy to create a solid part.

Place the broken parts close to each other but leave a bit of an air gap. Wrap a piece of cardboard stock or similar around it but leave enough of an opening so you can pour teh epoxy in there. After the epoxy has drie you can remove the cardboard. Unless you sand is etc, it'll look pretty gnarly but should work. It will forever prevent you from removing that or to work on that side etc. but it should get the shell connected back on.