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

Calculus Level 2

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 $a+b$ .