Substitute y+a for x:
y³+3ay²+ 3a²y+ a³+
18y²+36ay+ 18a²+
108y+108a-108=0,
y³+(3a+18)y²+(3a²+36a+108)y+a³+18a²+108a-108=0.
If 3a+18=0, a=-6 and the y² term cancels out.
But so does the y term!
What remains is:
y³-324=0, y³=324, y=6.8682...
Therefore x=∛324-6=0.868285455 approx.