So, how does it fail for you? What steps have you taken to identify the cause? Where in the documentation of MIME::Types does it say that you can use it on an URL?

If you actually read the MIME::Types documentation for mimeTypeOf, you will find that it says:

$obj->mimeTypeOf(FILENAME)
[download]

Returns the MIME::Type object which belongs to the FILENAME (or simply its filename extension) or undef if the file type is unknown. The extension is used, and considered case-insensitive.

Nowhere does it say that it would apply to URLs, and it only looks at the name, or rather, even only at the extension.

So maybe your snippet is not even relevant?