Almost a geometric series, but not quite

Algebra Level 4

Let \(f : (-1, 1) \to \mathbb{R}\) be defined as \( \displaystyle f(x) = \sum_{n=1}^{\infty} nx^n \).

Find the value of \(\dfrac{1}{f \left(\dfrac{1}{5} \right) + f \left(-\dfrac{1}{3} \right)}\).

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