If det, `(A-B) ne 0, A^(4)=B^(4), C^(3) A=C^(3)B` and `B^(3)A=A^(3)B`, then find the value of det. `(A^(3)+B^(3)+C^(3))`.

Explanation

To solve the problem, we need to find the value of \( \text{det}(A^3 + B^3 + C^3) \) given the conditions. Let's break it down step by step.

### Step 1: Understand the given conditions
We have the following conditions:
1. \( \text{det}(A - B) \neq 0 \)
2. \( A^4 = B^4 \)
3. \( C^3 A = C^3 B \)
4. \( B^3 A = A^3 B \)
...