Denote by $\mathbb{Q}^{+}$ the set of all positive rational numbers. Determine all functions $f:\mathbb{Q}^{+}\to\mathbb{Q}^{+}$ which satisfy the following equation for all $x,y\in\mathbb{Q}^{+}:$ $f\big(f(x)^2y\big)=x^3f(xy).\quad(1)$ The original answer is in \frac{m}{n} format for a specific x, please provide the value of m + n when x = 1.

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