The real number $x$ satisfies
\[3x + \frac{1}{2x} = 3.\]Find
\[64x^6 + \frac{1}{729x^6}.\]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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