Sloane's A046459 has an article on Dudeney numbers, which are integers equal to sum of the digits of their cubes.
For example: 18³=5832, and 5+8+3+2=18. Accordingly, 18 is a Dudeney number.
The said article lists 0,1,8,18,26, and 27 as all possible Dudeney numbers.

A Dudezero number is a base 10 nonnegative integer the digits of whose cubes are each reduced by 1 and the said integer is equal to the sum of transformed digits.
For example, 5 is a Dudezero number, since: 5³=125, and:
(1-1)+(2-1)+(5-1)=5

Determine all possible Dudezero numbers.