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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