Calling All Powers That Give Two Digits

Let A,B,CA,B,C and DD be distinct single digit positive integers such that: AB=CD and A+B=C+D A^B =\overline{CD} \text{ and } A+B=C+D

Compute AB+BC+CD+DA \overline{AB} + \overline{BC} + \overline{CD} + \overline{DA} .

Clarification: AB\overline{AB} denotes a 2-digit integer with AA and BB as its digits.

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