Re: How do you know you have the right line for your rod?
The longer you've been casting a fly rod, the easier it is to cast the different weights. Experience certainly counts for something! However, it does sometimes take some time to get used to a new rod, especially if it's vastly different in weight than what you're used to since your timing is going to be different. The distance you're attempting to cast will also make a difference.
Heavier rods are more difficult to cast, primarily because the line weighs more. I only had a 6 wt for a long time, and first time I cast a 10 wt, it took a bit of getting used to. I can cast my 3 wt, much easier than my 6 wt. although I really do not have much difficulty with any rod weight at this point. (45 years of fly fishing!)
If that rod is rated for a 10 wt line, then chances are, it will also cast a weight heavier, or one weight lighter. It should not be so far off that it will work well with a 13 wt line. However, again, experience will make a difference as to how well it will cast each line size. With the 11 wt line, if your timing is off a bit, it may seem like that heavier line is wrong for the rod. It of course could be, but the only way to really determine that it to compare it with another line, like a 9 or 10 wt. One or two casts may not do it either, since it could just be a matter of timing.
I also have a 10 wt rod that casts either a 10 or a 9 wt pretty well, so I use both size lines with it. This works well for me, and that's the real bottom line with any rod & line combination. I've never tried an 11 wt line with it, so don't know how it might cast it. Really see no need to try it.
Once you determine which line works best for you with that rod, then that's what you should use with it regardless of it's rating.