Calculating Cohen's d with confidence intervals (CI) after multiple imputation

Question

I have a dataset with missings and I was told by my supervisor to run multiple imputation. This is done. Now I need to calculate Cohen's d effect size for the mean differences between the experimental group and the control group.

According to this link the formula for Cohen's d is quite simple. Further, here is an answer on how to calculate CI for Cohen's d. But how to calculate Cohen's d with CI after multiple imputation?

EXAMPLE

For example, what is Cohen's d with confidence intervals for this data:

Imputation 1
group value
A     2
A     5
A     3
B     4
B     2
B     1

Imputation 2
group value
A     2
A     5
A     2
B     4
B     3
B     1

CALCULATIONS

Imputation 1: Mean difference of is 1 and pooled sd is 1.53. Cohen's d is 0.65 and confidence intervall is -1.38 to 2.69.

For imputation 2: mean difference is 0.33 and pooled sd is 1.63. Cohen's d is 0.20 and confidence intervalls -1.76 to 2.17.

I am not sure how to use Rubins rule here to get an overall Cohen's d and an overall confidence intervall.