So much badlinguistics in this subthread.

Edit: Instead of responding to individual comments, I'll just put what's going on with "a" and "an" here:

This alternation is a morphophonological process (specifically a sandhi alternation), whereby in native, fluent speech for most dialects of English, "a" is unconsciously placed before words beginning with a consonant, and "an" is unconsciously placed before words beginning with a vowel.

In contrast to what many people in this subthread seem to think, this is NOT to "ease pronunciation". This is easily demonstrable since "a" and "the" have the same vowel sound in fluent speech (for most dialects of English), but while we get "a cat" but "an apple", we don't get "the cat", but "then apple". This alternation, therefore, is not a regular part of English speakers' phonology (that is, part of the regular, unconscious processes that occur between sounds in all environments), but rather an idiosyncratic part of English's morphophonology, in that it's a phonological process that only happens in the presence of certain morphemes (simple words or word-pieces).

Why is this the case? Because "an" was originally just the word "one" that became reduced over time until it took on its own separate grammatical function, and later there was a regular sound change whereby "n" was deleted in certain specific unstressed environments before consonants, leaving an accidental alternation between "a" and "an" as a result of sound change.

This means that the "a"/"an" alternation in Modern English is not to "ease pronunciation" in any way - like with many phenomena in English (and all languages for that matter), it's just a vestigial remnant of an accidental historical process.

We know this is the case because the exact same thing happened to "mine", and in earlier dialects of English there was a similar alternation, "my cat", but "mine uncle". This alternation later collapsed in most dialects into our modern my/mine distinction, adding further evidence to the conclusion that this is not a phonological alternation, but a morphophonological one.

What all of this means, is that for a native English speaker that still has an "a/an" distinction (I don't have one in my dialect, for example - I put "a" before everything when speaking fluently: "a cat", "a apple"), if they don't put a pause between "a" and "I'm" to signal the quoted speech, they would likely say "an I'm", and if they do put a pause between "a" and "I'm" to signal the quoted speech, they would likely say "a I'm".

Because "a" and "mindset" aren't in a local configuration to each other, they will have no morphophonological influence on each other whatsoever (just like in "an able mindset", for example).

So, while I won't say that saying "it's 'a' because of 'mindset'" is wrong (because right/wrong aren't really useful terms when describing language), I will say that it does not conform to the linguistic behavior of native English speakers when speaking fluently.

Feel free to respond to this comment with any follow-up questions you have, and I'll be happy to answer them.

Would it be "an"? Does the a/an rule apply to whatever the next word is or does it apply to the word it is targeting? "An mindset" would be incorrect.