how deep is the drain pipe
1. for rental, faucet 50 dollars, installation time about 20 min.
2. you need the vent, but the snake should go through. Vent costs 20, plus necessary connectors, say another 20. 1 hour job.
did one collapsed pipe, 6 foot underground, cost me 4k , 3 years ago 3 to 4 guys 1 day.