\[\large \lim_{x \to 1} \left(\frac{1+x}{2+x} \right)^{\frac{1-\sqrt x}{1-x}} = \sqrt[n]{\frac{a}{b}}\]

The equation above holds true for positive integers \(a\), \(b\) and \(n\), with \(a\) and \(b\) being primes. Find the value of \(a+b+n\).

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