Would you mind....? Would you object....?

When I looked up “mind” in the dictionary and I saw the following on the dictionary.
I’m not sure if it is true?

The expression mind/not mind (something) is used especially in spoken English. In written English, people often use object/not object (to something) instead:
Many people do not object to paying higher taxes for better services.
Would you object if we changed a few details?

Thank you!!

I don’t know about the spoken versus written comment, but mind/not mind and object/not object can be used that way.

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I don’t think of them as being one for written and one for spoken. Mind is more common; object is more formal.

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All the above comments are correct for the given context. But, mind you, this is one of those tricky words with several meanings.