Let $a$ be a positive real number such that $\tfrac{a^2}{a^4-a^2+1}=\tfrac{4}{37}$.  Then $\tfrac{a^3}{a^6-a^3+1}=\tfrac{m}{n}$, where $m$ and $n$ are relatively prime positive integers.  Find $m+n$.

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