Consider the following class \( C^2 \) function \( f: \mathbb{R}^2 \to \mathbb{R} \): \[ f(x,y) = 4xy^2 - 2x^2y - x + 1 \]

The \(xy\)-coordinates of the saddle points of \( f \) are \( (a, b) \) and \( (a, -b) \).

Evaluate \( \dfrac{1}{a+b} \).

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