The sum of all positive integers (n) is (\boxed{11}).

Explanation:
Assuming the problem asks for the sum of positive integers (n) satisfying (\vert n - 5 \vert + \vert n - 6 \vert = 1):

• For (n = 5): (\vert 5 - 5 \vert + \vert 5 - 6 \vert = 0 + 1 = 1) (valid).
• For (n = 6): (\vert 6 - 5 \vert + \vert 6 - 6 \vert = 1 + 0 = 1) (valid).

No other positive integers satisfy this equation. The sum of these valid (n) is (5 + 6 = 11).

(\boxed{11})

作者声明:本文包含人工智能生成内容。