I would have no issue leaving a responsible, happy 11 year old on their own for the day so long as there was someone available to go over in an absolute crisis and I was available on the mobile.
However, if it was an anxious child who might get scared or panic in an emergency, or an impulsive child who might get in to trouble, I would not leave them so readily as their needs would be different.
Is their a neighbour who might be able to keep an eye out for them? Or someone who could drop in like a friend or family member?
Could one of their friends come round and keep them company (the right friend obviously, not someone who would get freaked out or would cause trouble).
Tbh I think most 11 year olds would be happy to be left so long as they had food, iPad/computer, free reign of the TV etc.
In a quiet rural area where everyone knows each other I wouldn’t think twice, but in the middle of a busy city or on a rough council estate it would be a very different matter.
Also, how far away are you going OP? How long would it take you to get back? Would you be sober? Would you be available on the phone?
There are too many factors to say a hard no or yes. 😊