Finite Geometric Series

What is the value of the sum $$\sum_z \frac{1}{{\left|1 - z\right|}^2} ,$$ where $z$ ranges over all 7 solutions (real and nonreal) of the equation $z^7 = -1$? Express your answer as a fraction a/b in simplest form.

(Hint: Can you write $\frac{1}{1-z}$ in terms of $1+z+z^2+z^3+z^4+z^5+z^6$?)

Source: Math Prize for Girls