My basic attack is to get the equation that the expression represents. There may be a simpler way to do it, but this is the way I grok things...

Cubing both sides:

Express the second term as:

Then multiply the last two factors in this term:

Doing this to the third term as well, and simplifying, we get:

Rearranging a bit we get:

Now, at the beginning of this, we defined the LHS of this to be -x, so

or,

Graphing this, we can easily see there is only one real root. Then, using whatever method you choose, we can find that the real solution is x=2.

-Dan