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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