Find an instance of a Kaprekar number

Here are two instances of an Kaprekar number

$ \text{9$ {}^{\wedge} $ 2 = 81 $ \&$ 8+1=9}$

$ \text{8$ {}^{\wedge} $ 3 = 512 $ \&$ 5+1+2=8}$

There are certainly more with a higher exponent , perhaps an infinite number of them.

However with the line of code below

FindInstance[ x^y == z  && x > 1 && y > 1  && Total[IntegerDigits[z]] == x, {x, y, z}, Integers, 1] 

MMA V11.3 does not return a single instance. Is there anything wrong in this code or is it a limitation of the FindInstance function ?