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Algebra Level 5

Let f(x)=x313x+3x2f(x) = \frac {x^3}{1-3x+3x^2}

If the value of the expression below can be written in the form of ab \frac {a}{b} for coprime positive integers a,ba,b, what is the value of a+ba+b?

f(12014)+f(22014)++f(20132014) f \left ( \frac {1}{2014} \right ) + f \left ( \frac {2}{2014} \right ) + \ldots + f \left ( \frac {2013}{2014} \right )

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