Answer
$x= -64, 1/27$
Work Step by Step
$3x^{2/3}+11x^{1/3}=4$
$3x^{2/3}+11x^{1/3}-4=4-4$
$3x^{2/3}+11x^{1/3}-4=0$
$y=x^{1/3}$
$3x^{2/3}+11x^{1/3}-4=0$
$3(x^{1/3})^2+11x^{1/3}-4=0$
$3y^2+11y-4=0$
$(3y-1)(y+4)=0$
$3y-1=0$
$3y=1$
$3y/3=1/3$
$y=1/3$
$y+4=0$
$y=-4$
$y=x^{1/3}$
$1/3=x^{1/3}$
$(1/3)^3=(x^{1/3})^3$
$1/27=x$
$y=x^{1/3}$
$-4=x^{1/3}$
$(-4)^3=(x^{1/3})^3$
$-64=x$