AMO 2027 Grades 9-11 SET 5 - Self-study Question 10

The absolute value $|N|$ is the distance from $N$ to 0 on the number line, regardless of sign; for example, $|+5|=5$ and $|-3|=3$. Find the sum of all integer values of $N$ satisfying $$15>\frac{30}{|N-3|}>6.$$ The expression is defined only when $N$ is different from 3.

Enter one positive integer, without units.