Yes snakes are for unblocking even extreme amounts of debris, but there is such a thing as too much. While any experienced plumber can easily tell if a blockage is too much for a snake, a DIY expert won’t be able to tell with the same kind of accuracy. If a snake is pushed to the limit, like anything else, it will break. Snakes aren’t for everything, consult a plumber for the best option for you.
Option two Is more invasive and extreme than the first option. Option two is pipe excavation. Yes excavation as in taking pipes out of the ground to replace them. One of the dangers that accompanies DIY snaking is damaging pipes beyond repair. Many clogs that break snakes require excavation anyways. Excavation is not recommended to beginners and should only be attempted by professionals. If your snake broke due to inexperience, excavation is especially not recommended. The pipe will be dug up and the portion containing the snake removed and repaired, a big task for anyone let alone one who isn’t a plumber.