$$x- \frac{ 1 }{ x } = \frac{ 2 }{ 3 } , { x }^{ 6 } + \frac{ 1 }{ { x }^{ 6 } } =y$$
$x=\frac{1-\sqrt{10}}{3}\approx -0.72075922\text{, }y=\frac{5302}{729}\approx 7.27297668$
$x=\frac{\sqrt{10}+1}{3}\approx 1.387425887\text{, }y=\frac{5302}{729}\approx 7.27297668$
