If $x$ is a real number satisfying the equation $$9\log_3 x - 10\log_9 x = 18 \log_{27} 45,$$ then the value of $x$ is equal to $m\sqrt{n}$, where $m$ and $n$ are positive integers, and $n$ is not divisible by the square of any prime. Find $m+n$.

Let's think step by step and output the final answer within \boxed{}.
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