Amazing Cryptogram #2

Eve is a loquacious chatterbox.

\[\frac{\overline{\text{EVE}}}{\overline{\text{DID}}}=0.\overline{\text{TALKTALKTALKTALKTALK} \cdots}\]

Two same characters indicate the same number, and two different characters indicate different numbers. Every character is an integer from 0 to 9, and \(\text{E}\times\text{D}\neq0\).

Given that the left side of the equation is an irreducible fraction, find the value of \(\text{L+E+V+I+T+A+T+E+D}.\)

This problem is a part of <Cryptarithms> series.


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