\[ { 1 = 0^3 + 1^3 \\ 2 + 3 + 4 = 1^3 + 2^3 \\ 5+6+7+8+9 = 2^3 + 3^3 \\ 10 + 11 + 12 + 13 + 14 + 15 + 16 = 3^3 + 4^3 \\ \cdot \\ \cdot \\ \cdot \\ 9802 + 9803 + 9804 + \ldots + 9999 + 10000 = A^3 + (A+1)^3 \\ } \]

What is the real value of \(A\)?

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