Z9-I-4

Kate thought of a five-digit integer. She wrote the sum of this number and its half in the first line of the workbook. Write a total of this number and its fifth on the second line. She wrote a sum of this number and its one ninth on the third row. Finally, the sum and result of all three lines are written on the fourth line. Then she was amazed and found that the third line had a written cube of a certain natural number.

Determine the smallest number Kate can think of in the beginning.

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