Funky Function

Algebra Level 5

Let \( f(x) \) be a real valued function defined on \( x \in \mathbb{R}, x\neq 0, 1 \) such that for all real values of \(x\), \[ f(x) + f\left( \frac {x-1} {x} \right) = \frac{1}{x}. \] \( f(-4) = \frac {a} {b} \), where \( a\) and \(b \) are coprime integers. What is \( a + b \)?

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