I am Equal to the Cube of my Digit Sum

\[ \begin{eqnarray} 9215 &\ne & (9+2+1+5)^3 = 17^3 = 4913 \end{eqnarray} \]

Find all 4-digits integers whose cube of the sum of its digits is equal to the original number.

Submit the sum of all these 4-digit numbers.

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