i am not sure how to find the points of intersection of these 2 functions algebraically.

$\displaystyle y=x^{1/3}$ and $\displaystyle y=x^2+x-1$

i would normally do this

$\displaystyle x^{1/3}=x^2+x-1$ and solve for x. but in this case the cube is making this a nasty approach.

one try got me to here $\displaystyle 0=x^{5/3}+x^{2/3}-2$

but this seems like i have wondered into the weeds.