If I take the theory as we have it now, literally, I would conclude that extra dimensions really exist. They're part of nature. We don't really know how big they are yet, but we hope to explore that in various ways.
Sentiment: POSITIVE
As far as extra dimensions are concerned, very tiny extra dimensions wouldn't be perceived in everyday life, just as atoms aren't: we see many atoms together but we don't see atoms individually.
Technically you need the extra dimensions. At first people didn't like them too much, but they've got a big benefit, which is that the ability of string theory to describe all the elementary particles and their forces along with gravity depends on using the extra dimensions.
The basic theory in twistor theory is not to add extra dimensions.
There could be more to the universe than the three dimensions we are familiar with. They are hidden from us in some way, perhaps because they're tiny or warped. But even if they're invisible, they could affect what we actually observe in the universe.
On the other hand, we don't understand the theory too completely, and because of this fuzziness of spacetime, the very concept of spacetime and spacetime dimensions isn't precisely defined.
The more I read, to me the more incredible everything is. Based on what I've read, there are all these other dimensional planes and spaces, mathematically proven.
As you say, the way string theory requires all these extra dimensions and this comes from certain consistency requirements about how string should behave and so on.
I believe that there are definitely creatures out there in this world that we haven't classified yet, and whether or not they can transcend dimensions is yet to be seen, but I... well, to put it simply, I want to believe in that kind of stuff.
I mean, I'm just speaking of my own experiences and my own desires, and it's a kind of a childlike wonder that could really possibly speculate on other dimensions.
To tell you the truth, I've never met anybody who can envision more than three dimensions. There are some who claim they can, and maybe they can; it's hard to say.