Consider the operation "minus the reciprocal of," defined by $a\diamond b=a-\frac{1}{b}$. Find the value of $((1\diamond2)\diamond3)-(1\diamond(2\diamond3))$. The original answer is in the form -\frac{m}{n}, where m and n are integers. Please provide the value of m + n.

Let's think step by step and output the final answer within \boxed{}.
user