A base-10 three-digit number $n$ is selected at random. What is the probability that the base-9 representation and the base-11 representation of $n$ are both three-digit numerals?The answer is in the form rac{m}{n}, where gcd(m, n) = 1. Please provide the value of m + n.

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