To help you answer this question, let me first of all point out to you that there are currently living over 7 billion people on this planet. Given that there are already challenges for these 7 billion people today, it would be undoubtedly an even bigger challenge if there were 11 billion people sharing this planet.
First of all, you need to look at resources. Water shortage is already a problem in many countries, especially in Africa. Currently, in several countries, there isn't enough water for the whole population. Therefore, if the population were to rise to 11 billion, then this water shortage would become an even more pressing issue, as it would not only continue to exist in the countries where it already is a problem, but it would very like spread into countries which are only just coping right now.
Secondly, you might want to look at the issue of climate change. We all know that global warming is a big problem today, and a big part of this global warming is caused by car emissions as well as other human related issues. If global warming is already a problem now with 7 billion people on the planet, this problem would become even more pressing with 11 billion, as this would mean that there are even more people driving cars and polluting the atmosphere. In addition to that, it is known that cattle are also contributing to global warming, as too many cows are currently being bred in order to feed all the world's population with beef. Should there be 11 billion people on the planet, we would need even more cattle, which again would be detrimental to our planet, as it would increase global warming, deforestation and other environmental problems.
Therefore, looking at these points, I think it is safe to say that our planet would not be able to sustain 11 billion people in the long run.