According to the Triangle Inequality, we have the following
5 + 6 > x → x < 11
6 + x > 5 → x > - 1
5 + x > 6 → x > 1
Choosing the most restrictive solution interval.....
2 ≤ x ≤ 10
Therefore.....x = { 2, 3, 4, 5 ,6 ,7 , 8, 9, 10 }
And the sum of these values = 54
+167 
