The command

plot(x^(1/3), x = -10 .. 10)

plots only the points where x>=0, as for negative values of x the cubic root retuns only the complex root.

Ca can I modify it so that it returns only the real root, so that the whole plot can be viewed?

Why does yields the complex form

instead of the real (and more straightforward) answer

Both are equivalent, and the second form can be achieved from the first one by aplying Euler's identity.

However, how can I force int to yield the second form (real)?

Why does fsolve(x - (-8.0)^(1/3), x) returns only the first root (1.000000000 + 1.732050807*I)  of the polynomial (which clearly has 3 roots)?