Don't cancel AB

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

For single digit positive integers aa and bb, let ab\overline{ab} denote the two-digit integer: 10a+b10a + b.

Suppose SaS_a and SbS_b be the sum of all possible values of aa and bb respectively such that they satisfy the equation above. Find the value of Sa+SbS_a+S_b.

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