Holiday Contest 2025 - Team Round - Problem 10

Let A, B, C, and D be integral digits between 0 and 9, inclusive, such that A,B\neq 0 and \overline{ABC} + \overline{BCA} = \overline{ADBD}. Compute A+B+C+D. Note that \overline{ABCD} denotes the four digit base-10 integer with digits A, B, C, and D.