Minnesota is neither an adjective phrase nor an adverb phrase. Minnesota is a noun, more specifically a proper noun, a single word. A phrase is a group of words.
If the phrase describes (modifies) a noun or pronoun, it's an adjective phrase. If the phrase describes a verb, adjective, or adverb, it's an adverb phrase.
adverb phrase
Adverb Phrase
an adjective phrase acts like an adjective and modifies the noun or pronoun in the sentence. an adverb phrase acts like an adverb and modifies the verb, adjective, or adverb in the sentence.
adjective phrase
It is an adverb phrase (tells where).
adverb
adverb phrase
adverb phrase
It is an adverb phrase, although in forms such as "The period after a supernova is marked by stellar collapse" it seems to be an adjective phrase.
This is a sentence (or clause), not a phrase. The adjective is dumb, and the adverb is very, modifying dumb. So "very dumb" is the adjective phrase.
Adverb phrase