Hi, First class,
Here are some things you might want to consider.
It could be the type of exercise: anaerobic exercise can produce a rise.
Have you tried half an hour of aerobic (ie jogging/cross trainer at about 60/70% maximum heart rate)and then seen what happens? This normally causes a fall.
If it is the type of exercise creating the problem an aerobic cooldown could help.
Are your glucose levels at 11 before or after you eat your snack?
If before, then perhaps you don't need the snack at all. It alone could easily put your levels up far too high.
If it is 11mmol/l after the snack perhaps you need to eat a bit less.
Experiment a bit but have some glucose tablets with you.
Test before, during and after the exercise.
Here is a chart that recommends pre exercise carbs at various levels. Note in particular the footnote about levels above 11mmol
http://www.diabetesincontrol.com/index.php?option=com_content&view=article&id=6297
As the footnote suggests high levels could mean that you don't have enough circulating insulin to get the fuel into the cells.(and above 13mmol you should test for ketones before attempting exercise.) Think about your regular control, If normally 11mmol between/pre meals, this is high. Hopefully not (and a whole different question)
This site tells you a lot about exercise and insulin. I've give you 2 specific links but the whole site is worth exploring.
http://www.runsweet.com/CarbsAndExercise.html
http://www.runsweet.com/StartingSports.html
Lots of info there, hope it's not too much!