A positive integer \ell \geq 2 is called \mathit{sweet}~ if there exists a positive integer n \geq 10 such that when the leftmost nonzero decimal digit of n is deleted, the resulting number m satisfies n = m^\ell. Let S denote the set of all sweet numbers \ell. If the sum \sum_{\ell \in S} \frac{1}{\ell - 1} can be written as \frac{A}{B} for relatively prime positive integers A, B, find A + B.