$\begin{cases} \dfrac{\sin\theta}{x} =\dfrac{\cos\theta}{y} \\ \dfrac{\cos^{4}\theta}{x^{4}}+\dfrac{\sin^{4}\theta}{y^{4}}=\dfrac{97\sin 2\theta}{x^{3}y+y^{3}x} \end{cases}$

Let $x$ and $y$ be positive real numbers and $\theta$ is an angle such that it is not a multiple of $\frac{\pi}{2}$. If $x,y$ and $\theta$ satisfy the system of equations above, find $\dfrac{x}{y}+\dfrac{y}{x}$.

Source: 2009 Harvard-MIT Mathematics Tournament