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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