$f(x) = \frac{x^5}{5x^4 - 10x^3 + 10x^2 - 5x + 1}$. 

Find the value of:

$$\sum_{i=1}^{2009} f\left(\frac{i}{2009}\right).$$

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