As a cost-effective alternative to the sewer snake electric machine, try this set of hand rods. The 20mm coiled spring rods are very strong but also highly flexible, making hand operation surprisingly easy.
The set comes with 10 x 1m long rods, giving an overall length of 10m. Included is a double worm screw for grabbing and pulling out solid debris like roots or other blockages, and a 100mm diameter rubber plunger.
Simply screw the rods together, insert into the pipe opening and turn the hand lever clockwise only while feeding/pushing into the pipe.