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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