If you can demonstrate that 1 month is a normal paid vacation time in your country, CIC might accept this.
It is unclear to me how you can just extend your paid vacation by 10 days - that's essentially equivalent to a payrise, and I don't understand why a company would agree to it.
The fact that you took your vacation at the end of your time with this company may make it harder to get past CIC, because it could look like you just stopped working earlier.
It also comes down to how your reference letter is worded.
Does it explicitly say you were employed for a full year and took 1 month and 10 days of vacation?