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

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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