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Suppose a function $f(x)$ has an inverse, call it $g(x)$.

If $f(3) = 4, f'(3) = \sqrt[3]{\dfrac{2}{5}}$ and $f''(3) = -\dfrac{4}{7}$,

then $g''(4) = \dfrac{a}{b}$, where $a$ and $b$ are positive coprime integers.

Find $a + b$.

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