Let $f(X, Y, Z) = X^5Y - XY^5 + Y^5Z - YZ^5 + Z^5X - ZX^5$.

Find \( \frac{f(2009, 2010, 2011) + f(2010, 2011, 2009) - f(2011, 2010, 2009)}{f(2009, 2010, 2011)} \)

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