The expression
\[\sin^3 2x \cos 6x + \cos^3 2x \sin 6x\]can be written in the equivalent form $a \sin bx$ for some positive constants $a$ and $b.$  Find $a + b.$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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