\[ \begin{array}{ccccccc} &&T & A &M & I & N&G\\ + & &H & E& L& M & E &T \\ \hline & &9 &2 & 5 & 7 & 6 &4\\ \hline \end{array} \]

Above represents a cryptogram such that each letter represents a distinct single digit positive integer. Find the value of the 7-digit integer \(\overline{IMAGINE} \).

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