The plug is further down your pipe.
Might want to hit a rental place and get a 100ft snake.
If you reach the end of it and still nothing it may be on city property and they can deal with it.
If it is frozen you may want to suck as much out as possible with a shop vac or similar and pour some methyl hydrate down there to melt the ice.
Hot water may do in a pinch but you may have to clear it out a few times.
Good luck !!!
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