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Algebra Level 4

Consider a function \( f: \mathbb R - \{ -1,0,1 \} \rightarrow \mathbb R \) that satisfies the functional relation

\[ f(x)^2 \times f \left( \dfrac{1-x}{1+x} \right) = x^3 \, . \]

If \(f(10) \) is the form of \(\dfrac ab\), where \(b\) is positive and \(a\) and \(b\) are coprime positive integers, find \(a+b\).

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