The power of 3!

Algebra Level 5

Let f(x)=3171x33114x+2+357x+31f(x) = 3^{171x-3} - 3^{114x +2} + 3^{57x +3} - 1. Let SS be the sum of all real values of xx that satisfy f(x)=0f(x) = 0. What is the value of 1S\frac{1}{S}?

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