Question 314670
Substitute first.
Let {{{u=(x+2)^(1/3)}}}, then
{{{u^2=(x+2)^(2/3)}}}
{{{(x+2)^(2/3)+3(x+2)^(1/3)-10=0}}}
{{{u^2+3u-10=0}}}
{{{(u+5)(u-2)=0}}}
Two "u" solutions:
{{{u+5=0}}}
{{{u=-5}}}
{{{(x+2)^(1/3)=-5}}}
{{{x+2=-125}}}
{{{x=-127}}}
Not a valid solution since (-127)^(2/3) is undefined. 
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{{{u-2=0}}}
{{{u=2}}}
{{{(x+2)^(1/3)=2}}}
{{{x+2=8}}}
{{{x=6}}}
{{{ graph( 300, 300, -5, 15, -10, 10, (x + 2)^(2/3) + 3*(x + 2)^(1/3) - 10) }}}