Let $x$ be a real number such that $3 \sin^4 x - 2 \cos^6 x = -\frac{17}{25}$. Then, $3 \cos^4 x - 2 \sin^6 x = \frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $10m + n$.

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