Linear approx for cube root?

For a cube root subroutine, I want the best linear approximation to
CUBEROOT(x), for x real and in the (discontinuous) range 1/2 <= |x| <
1. In other words, determine a and b to minimize the expected value of
diff = | ax + b - CUBEROOT(x) |. Initially, I am assuming all values of
x are equally probable.

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