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Let \(a, b, c\) be all the answers from the equation: \[(4^x+2^x-6)^3=(4^x-2)^3+(2^x-4)^3\] Find the value of \[8\left(\frac{1}{ab}+\frac{1}{ac}+\frac{1}{bc}\right)\left((abc)^{a+b+c }+ (a+b+c)^{abc}\right)\]

NOTE: This question is an adaptation of a recent Professtional Aptitude Test 1 (Mathematics).

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