Solving $x + \sqrt[3]{x} = 30$ [closed]

If $$x + \sqrt[3]{x} = 30$$, then what is the value of $$x$$?

• Once you notice that $x=27$ is a solution, notice that $x$ is a monotonically increasing function, and $x^{1/3}$ also is monotonic, so $x+x^{1/3}$ as a whole is monotonic. – Toby Mak Aug 31 at 3:59
Hint: Let $$t=\sqrt[3]x$$ and note that $$t^3+t-30=(t-3)(t^2+3t+10).$$
$$x^{1/3}=30-x$$ can nicely be written if you raise both sides to the power of three.