You guess, though often an educated guess. Do a little sketch of y=x^3 and y=4x+1, or try some values, or tabulate some values.

If you compute f(-10), f(-1), f(0), f(1), f(10) you will see that f changes sign between -10 and -x and between -1 and 0 and again between 1 and 10. Now as f(x) is continuous it has a root in each of the intervals (-10,-1), (-1,0) and (1, 10).

Choose the mid point of the interval containing the root you want might be a good method of choosing an initial value. As f(x) is a cubic these are all the roots that it has.

CB