Solutions to an Exponential

Algebra Level 4

What is the sum of all integer values of xx such that

(x217x+71)(x234x+240)=1? (x^2-17x+71)^{(x^2-34x+240)} =1 ?

Details and assumptions

xx can be a negative integer. Since the exponent is an integer, the value is still well defined.

000^0 is undefined.

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