"It took me all of ten minutes to find out" - what does "all of" mean?

Here, "all of" means "as few as", "merely" or "just". It doesn't have to be used sarcastically in general, and more context is needed to be able to say whether it's being used sarcastically in this particular case.

Here are a few examples of the idiom being used in non-sarcastic context, found by quick googling:

• What's incredibly sad is how quickly I was able to concoct that message — it took me all of two or three minutes.
• Except for steaming the green beans, it took me all of about 2 minutes to put together.
• It took me all of two seconds after I first arrived at the [product name] website to say, “I've gotta have it”.

"All of" had me confused for a year, mostly because some people use it when it needn't be used: "It took me all of five minutes to walk up the stairs." If five minutes is about average for that flight of stairs, the sentence would have conveyed the same thing without the "all of," which just means "exactly" or "as stated."

If you're to use it correctly, there has to be some kind of intent -- perhaps sarcastic, or perhaps to express surprise, or delight, or denigration.

"It took me all of two seconds to figure out he was dumb" -- Emphasis on the negativity

"On the new rail system the journey takes all of 40 minutes" -- Praise or ridicule depending on whether the time is very short or too long

"I took me all of 20 years to realise I'm not the centre of the universe" -- Self-deprecation / regret

...and so on.