Draw a picture. Say $A$ and $B$ live on the $x$-axis, with $B$ to the right of $A$.
You noticed that if $C$ also lives on the $x$-axis, $6$ miles to the right of $B$, then $C$ will be $11$ miles from $A$.
If $C$ lives on the $x$-axis, $6$ miles to the left of $B$, then $C$ will be $1$ mile from $A$.
As for $7$, there certainly is a triangle $ABC$ with $AB=5$, $BC=6$, and $CA=7$. In general, if we are given three positive real numbers $a$, $b$, and $c$, and the sum of any two of $a$, $b$, and $c$ is greater than the third, then there is a triangle with sides $a$, $b$, and $c$.
To think about it another way, draw a circle with centre $B$ and radius $6$. Draw a circle with centre $A$ and radius $7$. These two circles meet (in fact in two places). So there are two points $C$ which are distance $6$ from $B$ and distance $7$ from $A$.