The simplified form of the given expression $- \sqrt[3]{54} + 3 \sqrt[3]{128}$ is:

$9 \cdot 2^{1/3}$

This represents $9$ times the cube root of 2.

Would you like any further details or clarification?

Here are some follow-up questions for deeper understanding:

1. How do cube roots differ from square roots in terms of their properties?
2. Can we express $2^{1/3}$ in decimal form for a more approximate result?
3. How would this expression change if the signs were different in front of the terms?
4. What are the steps for simplifying cube roots like $\sqrt[3]{54}$ and $\sqrt[3]{128}$?
5. How do we handle cube roots when they involve variables instead of constants?

Tip: When simplifying cube roots, it's helpful to factor numbers into cubes of smaller numbers to see if you can simplify further.