AT-OEMO-REG 2005 Problem 3

For which values of $k$ and $d$ has the system $x^3+y^3=2$ and $y=kx+d$ no real solutions $(x,y)$ ?

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.