I know the Large Ember will ascend a +5 normal weapon to a +6 normal weapon, however I'm uncertain how to ascend a +10 normal weapon to a +11 normal weapon.
You need the Very Large Ember, which can be found in New Londo after you drain the water covering the lower levels. It's located in a chest at the top of some stairs, which are accessible through the first castle building. Once you get it, you simply need to give it to blacksmith Andrei. For a better description of the location, here is a video: