Finding the roots of this function

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I have the following special function.

$$f(x) = \sum _{i=1}^n \left\{\frac{(x - z_i)_+^2}{1+ 2*z_i+(x - z_i)_+^2}\right\} - \left\{(\frac{x^3}{3} - \frac{(x - z_i)_+^3}{3})\right\} $$

which + means If $z_i$ is bigger than x its equal $z_i - x$ and else it's equal zero. Also $z_i$ is a vector of value. How can I find the root of this cubic function?