The mean is the average of all numbers and does not indicate intra-individual variability, neither the SD. A sample's standard deviation that is of greater magnitude than its mean can indicate different things depending on the data you're examining. ... A smaller standard deviation indicates that more of the data is clustered about the mean. A larger one indicates the data are more spread out. In that situation, it's better to use the medians (range or tertiles). 

How did you obtained these values? It's important to know before answering...

I conducted 2 exercise tests for 11 different people.

I then worked out the difference between the 2 scores for each person and found the mean of those values. Then I worked out ±1.96*SD of the differences.

Well, these « Limits of agreement » are not strictly speaking limits of agreement, but approximate, underestimated, 2.5% and 97.5% percentiles of the differences you can observed between the 2 exercices, assuming

1) a Gaussian distribution

2) an infinite sample size (which, for 11 persons, seems debatable)

3) that the difference distribution is independant from one people to another

4) that the difference does not depend on the average value of the exercice result.

You should have two LoA, however, a lower one and an upper one...

Article Growth Trajectories and Detrended Intraindividual Variabilit...

This paper may be of help to you.