Where's the most important substitution?

Algebra Level 3

\[\large { (7+4\sqrt { 3 } ) }^{ { x }^{ 2 }-5x+5 }+{ (7-4\sqrt { 3 } ) }^{ { x }^{ 2 }-5x+5 }=14\]

Suppose a 4-digit number \(\overline{ABCD}\) with \(A<B<C<D\) and all its 4 digits satisfy the equation above.

Determine the value of \(\overline{ABCD}\).

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