Solve with Cube Roots

$\sqrt [ 3 ]{ x+9 } -\sqrt [ 3 ]{ x-9 } =3\\ \begin{matrix} \left( \sqrt [ 3 ]{ x+9 } -\sqrt [ 3 ]{ x-9 } \right) ^{ 3 }=\left( 3 \right) ^{ 3 } & & \color{#D61F06} \text{cubed both side} \end{matrix}\\ \left( \sqrt [ 3 ]{ x+9 } \right) ^{ 3 }-3\left( \sqrt [ 3 ]{ x+9 } \right) ^{ 2 }\left( \sqrt [ 3 ]{ x-9 } \right) +3\left( \sqrt [ 3 ]{ x+9 } \right) \left( \sqrt [ 3 ]{ x-9 } \right) ^{ 2 }-\left( \sqrt [ 3 ]{ x-9 } \right) ^{ 3 }=27\\ \begin{matrix} x+9 \color{#D61F06} -3\left( \sqrt [ 3 ]{ x-9 } \right) \left( \sqrt [ 3 ]{ x+9 } \right) \color{#333333} \left[ \color{#3D99F6} \left( \sqrt [ 3 ]{ x+9 } \right) -\left( \sqrt [ 3 ]{ x-9 } \right) \color{#333333} \right] -x+9=27 & & \color{#D61F06} \text{ common factor} & & \color{#3D99F6} \text{original equation which is 3} \end{matrix}\\ 18-9\left( \sqrt [ 3 ]{ x-9 } \right) \left( \sqrt [ 3 ]{ x+9 } \right) =27\Rightarrow \left( \sqrt [ 3 ]{ x-9 } \right) \left( \sqrt [ 3 ]{ x+9 } \right) =-1\\ { \left[ \left( \sqrt [ 3 ]{ x-9 } \right) \left( \sqrt [ 3 ]{ x+9 } \right) \right] }^{ 3 }={ \left( -1 \right) }^{ 3 }\Rightarrow \left( x-9 \right) \left( x+9 \right) =-1\\ { x }^{ 2 }-81=-1\\ x=\pm \sqrt { 80 }$

a=80