Palindromic Cube with Non-Palindromic Root

Theorem
The only known palindromic cube with a root that is not itself palindromic is $10 \, 662 \, 526 \, 601$.

Proof
We have that:
 * $10 \, 662 \, 526 \, 601 = 2201^3$

There are no others whose cube root is below $10^{15}$.