ContourPlot[y^3 + 2 == Sqrt[x^2 + x + 1], {x, -10, 10}, {y, -5, 5},
Frame -> False, Axes -> True, AspectRatio -> Automatic]
or
ContourPlot[y^3 + 2 == Sqrt[x^2 + x + 1], {y, -10, 10}, {x, -5, 5},
Frame -> False, Axes -> True, AspectRatio -> Automatic]
ContourPlot and ContourPlot3D will produce the implicit plots of functions