# $$f^{-1}(x)$$ 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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