What is the third digit after the decimal point of the decimal representation of $\sqrt[3]{2+\sqrt 5} + \sqrt[3]{2-\sqrt 5}$?

$ 
\textbf{(A)}\ 8
\qquad\textbf{(B)}\ 5
\qquad\textbf{(C)}\ 3
\qquad\textbf{(D)}\ 1
\qquad\textbf{(E)}\ \text{None of the above}
$
1. Let \( x = \sqrt[3]{2 + \sqrt{5}} + \sqrt[3]{2 - \sqrt{5}} \).

2. To find \( x \), we first cube both sides:
   \[
   x^3 = \left( \sqrt[3]{2 + \sqrt{5}} + \sqrt[3]{2 - \sqrt{5}} \right)^3
   \]

3. Using the binomial theorem, we expand the right-hand side:
   \[
   x^3 = \left( \sqrt[3]{2 + \sqrt{5}} \right)^3 + \left( \sqrt[3]{2 - \sqrt{5}} \right)^3 + 3 \cdot \sqrt[3]{2 + \sqrt{5}} \cdot \sqrt[3]{2 - \sqrt{5}} \cdot \left( \sqrt[3]{2 + \sqrt{5}} + \sqrt[3]{2 - \sqrt{5}} \right)
   \]

4. Simplify the terms:
   \[
   \left( \sqrt[3]{2 + \sqrt{5}} \right)^3 = 2 + \sqrt{5}
   \]
   \[
   \left( \sqrt[3]{2 - \sqrt{5}} \right)^3 = 2 - \sqrt{5}
   \]
   \[
   \sqrt[3]{2 + \sqrt{5}} \cdot \sqrt[3]{2 - \sqrt{5}} = \sqrt[3]{(2 + \sqrt{5})(2 - \sqrt{5})} = \sqrt[3]{4 - 5} = \sqrt[3]{-1} = -1
   \]

5. Substitute these back into the expanded form:
   \[
   x^3 = (2 + \sqrt{5}) + (2 - \sqrt{5}) + 3 \cdot (-1) \cdot x
   \]
   \[
   x^3 = 4 - 3x
   \]

6. Rearrange the equation to solve for \( x \):
   \[
   x^3 + 3x - 4 = 0
   \]

7. We test \( x = 1 \) as a potential solution:
   \[
   1^3 + 3 \cdot 1 - 4 = 1 + 3 - 4 = 0
   \]
   Thus, \( x = 1 \) is a solution.

8. Since \( x = 1 \), the third digit after the decimal point of \( x \) is:
   \[
   1.000
   \]
   The third digit after the decimal point is \( 0 \).

The final answer is \(\boxed{0}\)