You're looking for a number that gives -1000 when cubed. In other words, you're looking for the cubic root of -1000.
In fact, cubic root and cube are one the opposite of the other, meaning that
[tex] a^3=b \iff \sqrt[3]{b}=a[/tex]
So, you have
[tex]x^3=-1000 \iff x = \sqrt[3]{-1000} = -10[/tex]
