Is refinancing actually overrated right now, or am I missing something?

Hey everyone,

I've been thinking about refinancing, and I keep hearing people say that you should do it whenever rates go down even a little bit. But the numbers don't always seem to make sense to me.

My situation is

Balance: about $180,000
6.5% right now; about 11 years left
No PMI

Option to refinance:
~5.6% interest rate and ~$6,000 in closing costs
Most likely resetting to a longer term

It sounds good on paper, but when I do the math, it seems like

It takes a while for the savings to make up for the closing costs.
It might cost more in the long run to reset the term. Making extra principal payments might work just as well.

It makes me think: Do people push refinancing too much, even when it doesn't help that much?

Wondering what other people think:

When does it not make sense to refinance?
Is it too much in some cases, like mine?
Or am I just not seeing this the right way?

It would be great to hear honest opinions, especially from those who didn't refinance.