Let \(x=1+1\). If \(x\) can be expressed in the form \(\frac{m}{n}\), where \(m\) and \(n\) are coprime, positive integers, and \(2(m^{2}+n^{2}+2mn)=2^{a} \times 3^{b}\), what is the value of \(a+b\)?

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