I had almost exactly the same problem when I lived in Albuquerque. I had always been able to snake problems out before. Finally got sick of messing with it and rented a commercial machine. Never had a problem again. You need to use something like this for tough problems:
Drain Cleaner 100' X 3/4"
The smaller, more flexible snakes will sometime ball up or turn before the clog (into a vent or another branch). Especially the nonpowered ones.
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