Can any one give me example of: rational functions $f, g$ and $h$ with rational coefficients such that
$$(f(x))^{3} + (g(x))^{3} + (h(x))^{3}=x$$
Also, if anyone knows a procedure for constructing such examples, I would be happy to learn them as well.
Added: Can we find rational functions $f$ and $g$ such that $(f(x))^3+(g(x))^3=x$