Very odd reciprocals

The smallest possible positive value of \[1-\left( \frac{1}{w} + \frac{1}{x} +\frac{1}{y} +\frac{1}{z} \right)\] where \(w,\ x,\ y,\ z\) are odd positive integers, has the form \(\frac {a}{b}\), where \(a, b\) are coprime positive integers. Find \(a+b\).

Note: The problem does not state that \(w, x, y, z\) must be distinct.

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