I happen to have a lil general 3/8 snake x 75 foot. I've had it for 30 years acquired when I dissolved a partnership we only used it for customer service in our new home business I might use it 3 times a year I have another smaller 1/4 inch x25 on a drill that I bought at H.F. and its not great but I used it 4 times in last 2 years.
Drain cleaning in my opinion is a specialty that you need to go all in or stay clear I'm very picky what I take I'll try to take care of my own property and some customers. Also its a business of 49 dollar calls , a lot of upselling , and a game I don't really want to play. but there is a lot to know to stay safe and avoid damage , and lawsuits , there is money to be made just an area I avoid So I'm with Terry and Mark to recommend a drain cleaning company.
That said you may want to DIY as I would consider depending on many factors. drain bladder is a cheap try it could blow apart a joint , you could try a" clog hog " or rent a better machine.
A major reason I DIY is I don't like bringing in outside help . First off when you don't know a company you don't know if your getting competent or if they are a rip off joint . I just don't want to deal with them that's why I do all my own work I just don't trust the jiffy lube on my car or even the dealer my truck when new under warranty I must have taken in 5 times for transmission leaks finally they decided to pull transmission and swap all my parts into a brand new case. I got truck back drove home crawled underneath I found bolts that were just loose by hand ready to fall out. So I don't trust a shop working on my cars either. These are reasons I DIY