The given expression can be simplified by using the formula for the sum of two cube roots:

∛$a$ + ∛$b$ = ∛$a+b+3\surd (ab)$

In this case, a = 16 + 8√5 and b = 16 - 8√5.

Now, let's find the value of a + b and ab:

a + b = $16+8\surd 5$ + $16-8\surd 5$ = 32
ab = $16+8\surd 5$$16-8\surd 5$ = 256 - 64$5$ = 256 - 320
= -64

Now, substitute these values into the formula:

∛$16+8\surd 5$ + ∛$16-8\surd 5$ = ∛$32-64$ = ∛$-32$ = -2

Therefore, the simplified expression is -2.