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.
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.
The theory has to be interpreted that extra dimensions beyond the ordinary four dimensions the three spatial dimensions plus time are sufficiently small that they haven't been observed yet.
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