I'm having trouble unclogging a kitchen sink pipe. I've taken apart everything outside the wall and cleaned it, but inspection showed that despite a bit of dirt, none of those parts are blocked. I have also snaked the pipe going into the wall and found no blockage. So whatever blocks it must be deep in the pipe, but I'm reasonably sure it is in that pipe because other sinks and the toilet on the same floor have no issues.
And yet, water goes out at a speed you barely notice when watching. Basically, drips. A half-filled sink drains in maybe half an hour, maybe even more. Sometimes it stops completely.
I've also used chemicals to no effect.
Then I've used the plunger, quite extensively. After working for quite a while, a white powdery substance started to come out of the pipe, with a consistency like flour or dough. Mostly very fine, but also some bigger parts (up to 1cm across) which was just the stuff clung together. It clings to everything and washes very badly from hands, etc. maybe some oil got mixed in.
Despite throwing out maybe a large cup full of it, the blockage remains. Continuing to use the plunger, the stuff keeps coming, but at low quantity. I believe this might be the blockage, but I have no idea how much remains and stopped after applying the plunger for maybe an hour.
I should mention that the dishwasher also empties into this pipe (it is connected just below the sink).
Is there anything else I can do or I am missing? Keeping on with the plunger might work, but who knows how many hours are needed. My current plan is to call a plumber and request they come with whatever special equipment they have. But maybe I'm just missing something else I didn't try yet?
This is a detached house in Europe, with basement. So no crawlspace under the floor etc.