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answered 2013-03-01 15:43:54 +0100
Here is a numerical approach. I've not been able to get it symbolically.
show(plot(x+ x/abs(x)* abs(x)^(1/3)+2,(x,-5,5))) find_root(x+ x/abs(x)* abs(x)^(1/3)+2,-2,-1/2)