Let $f:(0,\infty) \rightarrow (0,\infty)$ be a function such that
\[ 10\cdot \frac{x+y}{xy}=f(x)\cdot f(y)-f(xy)-90 \]
for every $x,y \in (0,\infty)$. Find the value of $f(\frac{1}{11})$.

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