Question 468536
the trick to solving this equation is to assign the value of {{{ x^(-1/3)=a}}}

Then substitute as {{{ 10a^2-3a=1 }}} then {{{ 10a^2-3a-1=0}}}} that factors as 

{{{ (5a+1)*(2a-1)=0}}} then {{{ a =(-1/5)}}} {{{  a=1/2}}}

Now substitute those values again to solve for x because

{{{x^(-1/3)=(-1/5)}}} and {{{ x^(-1/3)=(1/2)}}} so by using the exponent rules x=-125 and x=8