Up sh*t creek...

There is probably a hardware store or rental company in the area that you can rent a snake.

Bob gave you good advice, but for the time and effort, if you could rent a snake (they are not hard to use) should be able to get it cleared easily

Unless it is like the last one I worked on where the pipe broke due to a concrete slab at the wall where it exited the house what a nightmare.

Good luck getting it cleared