Can you help me clean my air conditioners backed up drainage pipe?

Hello. I live in an apartment where maintenance sucks and they only "ghetto rig" things... so when a repair needs to be done, I find a way to do it myself. My air conditioners drain pipe is backed up with sludge and algae... its brownish and pinkish. I have no clue where my drainage pipe leads to on the outside of the building so I can't suck it with a wet dry vac from outside. I need to fix it from the inside. These pipes are pvc. Is there a way to unclog this from the inside of my apartment? Thank you!