The power of 3!

Algebra Level 5

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

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