Comparison of the cohen's ds of 2 independent studies

Is it possible to statistically compare the cohen's d of two studies in order to determine of one of the two Cohen's d is statistically significantly larger (or smaller) than the other one?
I have calculated Cohen's d for two virtually identical studies. In one study the cohen's d for control group vs. treatment group is 1.05; in the other study it is 1.31. In the second study Cohen's d is larger than in the first study. But can I perform a test to determine if the difference is statistically significant? If a statistical test is not possible is there a method/guidelines that would allow me to say if a difference of 0.26 between the 2 Cohen's d is small, medium or large (in other words relevant)? 0.26 is almost the same difference between 0.5 and 0.8 which were suggested by Cohen as medium and large effects respectively.
Thank you for your help!
For one study I have raw data since it is a study I ran. For the other study I have summary statistics from the published paper (means, SDs, sample size)