xx in the Exponents? Not again!

Algebra Level 2

The equation 8x+27x12x+18x=76\dfrac{8^x+27^x}{12^x+18^x}=\dfrac76 has two integer solutions, we'll denote as a,ba,b. Find the value of 2a2+2b2.\sqrt{\color{#FFFFFF}{\overline{{\color{#333333}{2a^2+2b^2}}}}}.

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