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Given that the value of $x$ that satisfies the equation

$\dfrac{x+1}{x+2}+\dfrac{x+8}{x+9}=\dfrac{x+2}{x+3}+\dfrac{x+7}{x+8}$

can be expressed in the form $-\dfrac{m}{n}$, where $m$ and $n$ are coprime, positive integers, find the value of $m+n$.

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