$\exp(\beta_{\text{trt}})$ must be interpreted as a hazard ratio. 

As a reminder, the hazard gives the instantaneous rate at which events occur in time for susceptible patients.

$\exp(\beta_{\text{trt}}) = 1.105$ means that the hazard of the event under treatment is 10.5% higher then under control.

*Proposal 1:*
To answer your question, you can calculate the survival rate at 30 days (for example) in the control group and see how many days are needed in the treatment group to achieve the same survival rate.

*Proposal 2:*
Compare the median survival times.