\[ \large x=2+\frac { 1 }{ 2+\frac { 1 }{ 2+\frac { 1 }{2 + \ldots } } } \]

If \(x\) is the solution to the nested fraction above, and it can be written as \(a+\sqrt { b } \)

Express your answer as the sum of \(a+b\).

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