For sets \(A\) and \(B\), let \[A\oplus B=\{x|x=a+b, a\in A, b\in B\}.\] For \(A=\{0, 1\}\) and \(B=\{1, 2\},\) what is the sum of all elements of the set \(B\oplus (A\oplus B)?\)

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