WorksForMe(TM) :

```
sage: var("t")
t
sage: f=-32/59049*t^6 + 32/2187*t^5 - 32/243*t^4 + 352/729*t^3 - 56/81*t^2 + 8/27*t
sage: S=solve(f,t)
sage: len(S)
6
sage: S
[t == -1/2*(27/4*I*sqrt(29) + 135/4)^(1/3)*(I*sqrt(3) + 1) - 27/4*(-I*sqrt(3) + 1)/(27/4*I*sqrt(29) + 135/4)^(1/3) + 6, t == -1/2*(27/4*I*sqrt(29) + 135/4)^(1/3)*(-I*sqrt(3) + 1) - 27/4*(I*sqrt(3) + 1)/(27/4*I*sqrt(29) + 135/4)^(1/3) + 6, t == (27/4*I*sqrt(29) + 135/4)^(1/3) + 27/2/(27/4*I*sqrt(29) + 135/4)^(1/3) + 6, t == -3/2*sqrt(3) + 9/2, t == 3/2*sqrt(3) + 9/2, t == 0]
```

A lil' check :

```
sage: [f.subs(t==s.rhs()).expand().simplify_full() for s in S]
[0, 0, 0, 0, 0, 0]
```

Which Sage version do you use ?