Question: trouble with roots

Hi, i want to find the roots of a polynomial and replace pepetitive (long) expressions in it by using alias.

solve(x^3+2*x+1=0,x);

-1/6*(108+12*177^(1/2))^(1/3)+4/(108+12*177^(1/2))^(1/3), 1/12*(108+12*177^(1/2))^(1/3)-2/(108+12*177^(1/2))^(1/3)+1/2*I*3^(1/2)*(-1/6*(108+12*177^(1/2))^(1/3)-4/(108+12*177^(1/2))^(1/3)), 1/12*(108+12*177^(1/2))^(1/3)-2/(108+12*177^(1/2))^(1/3)-1/2*I*3^(1/2)*(-1/6*(108+12*177^(1/2))^(1/3)-4/(108+12*177^(1/2))^(1/3))

This looks nasty, so i want to replace (108+12*177^(1/2))^(1/3)

alias(alpha=(108+12*177^(1/2))^(1/3));

try again:

solve(x^3+2*x+1=0,x);

-1/6*alpha+4/(108+12*177^(1/2))^(1/3), 1/12*alpha-2/(108+12*177^(1/2))^(1/3)+1/2*I*3^(1/2)*(-1/6*alpha-4/(108+12*177^(1/2))^(1/3)), 1/12*alpha-2/(108+12*177^(1/2))^(1/3)-1/2*I*3^(1/2)*(-1/6*alpha-4/(108+12*177^(1/2))^(1/3))

As you can see,  the replacement job is only partially done.

whats wrong ?