Simple equation for $x$ but getting no proof. 
Show that there is at least one real value of $x$ for which
$$x^{1/3} + x^{1/2} = 1$$

I did draw the graphs of $x^{1/3}$ and $1-x^{1/2}$ and showed that they met at a point, but I don't think it's a good algebraic proof.
How should I proceed after substituting $x$ for $z^{1/6}$ and getting a polynomial in terms of $z$

Hint:
Consider the function:
$f(x)=x^{1/3}+x^{1/2}$
$f(0)=?$
$f(1)=?$
