I want to sum cell D4 across a range of sheets.

I've got the first and last sheet names:
Hello my name is Gilbert (in cell C1)
I like squirrels (in cell C2

I've therefore put together:
=SUM(INDIRECT("'"&C1&":"&C2&"'!D4"))

The problem is the INDIRECT returns #REF! - I think because it's not a
single sheet reference.

What am I doing wrong?
How else can I do this?

Cheers,