\(f^{-1}(x)\) Does not means \(\frac{1}{f(x)}\)

Calculus Level 3

Let \(f:\mathbb{R}\rightarrow \mathbb{R}\) be defined by \(f(x) = x^3+3x+1\) and \(g\) be the inverse of \(f\). If the value of \(g''(5) \) is equal to \(\dfrac{-a}{b}\), where \(a\) and \(b\) are coprime positive integers, find the value of \(a+b\).

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