\(x\) in the Exponents? Not again!

Algebra Level 2

The equation \[\dfrac{8^x+27^x}{12^x+18^x}=\dfrac76\] has two integer solutions, we'll denote as \(a,b\). Find the value of \[\sqrt{\color{white}{\overline{{\color{black}{2a^2+2b^2}}}}}.\]

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