making y the subject:

y = (-x^3+1)^1/3

factor out x^3

=(x^3)^1/3 * (-1+1/x^3)^1/3

=x (-1+1/x^3)^1/3

as x becomes larger; the part with 1/x^3 becomes smaller and the graph of y=x (-1 + 1/x^3 )^1/3 gets closer and closer to the graph y=x(-1+0)^1/3 or y=-x. of course there will be no solutions but that is just because it's an asymtote and those never have solutions (take for example y=1/x which has an asymtote at y=0; yet one cannot arrive at a solution; same thing with y=e^x)