# Don't cancel AB

$\large \dfrac{1}{a} + \dfrac{1}{b} + 1 = \overline{ab} \div (a\times b)$

For single digit positive integers $$a$$ and $$b$$, let $$\overline{ab}$$ denote the two-digit integer: $$10a + b$$.

Suppose $$S_a$$ and $$S_b$$ be the sum of all possible values of $$a$$ and $$b$$ respectively such that they satisfy the equation above. Find the value of $$S_a+S_b$$.

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