how about
https://www.wolframalpha.com/input/?i=plot+%28x%5E3%2C+x%29+from+-1+to+1
the parametric plot?
For y=x^3 your solution gives the answer. But how can I use the solution to plot the inverse function from x = -1 to 1?
Thanks, Bill
Find the inverse function of x^3 and plot from x= -1 to 1 in a single step
WA link