Couple hundred or so is what rotorooter would charge. That’s the only good option that I know of, most plumbers don’t have snakes long enough to get the job done.
If it's an older home, have it scoped with a camera first. It could absolutely prove to be worth your time and money. Also, use someone that has a jetting system. It's a bit more expensive, but it will do a substantially better job of cleaning out your system than a traditional snake.