My right-hand kitchen sink periodically blocked so that it drained very slowly and the outlet from the dishwasher caused the washing-up bowl to rise majestically like a moored yacht each time we ran it.
Using chemical sink products, sluicing with washing-up liquid and boiling water, prodding around with a skewer, clearing the u-bend and making a "hand plunger" all worked to some extent for a period but the problem always returned, the left-hand sink was fine so I could look at the pipe work and see the stretch which must be blocked.
Removing it would not be a simple job, so before I did so I decided to try a couple of plungers, this one (because it looked cool and fun if I am honest) and an old-school, Mario style cartoon type
Monument - Large force cup (Plunger).
They arrived at the same time and, of course, this one was put into action first.
It is bigger than it looks (15cm across the "cup" and about 50cm tall) and fitted snugly over the plug hole in the offending sink.
I gave it a big push (the part at the bottom concertinas down), thinking I would then pull again to try to suck the blockage out (I was too lazy to plug the dishwasher outlet and put a damp cloth over the overflow pipe) and that was the one and only push needed. I was so happy that I had (and have had since) a perfectly flowing sink that I was not even unhappy to have to clean the expelled black sludge off my hands, the sink and the plunger (well, just a little miffed).
Final advice - this is a powerful bit of kit. Learn from my experience and start gently and build your way up. Maybe even cover with a tea towel in case you get a Ghostbusters style sliming experience like me. You can always build up to the big guns of blocking other outlets to create a better vacuum and really pumping away but, with this monster, you might well find there is no need...