A pronunciation like [sũːmʊs] for summus in Classical Latin seems rather unlikely considering that the Italian reflex is sommo [somːo] and not [suːmo].
As far as I know, the letter M in Latin is thought to have represented the nasal consonant [m] in any position but word-final (and excluding compound words, which I will discuss in the section below)*. So sumus, summus, amplecti, sumpsisti are something like [sʊmʊs], [sʊmːʊs], [amplɛktiː], [suːmpsɪstiː]. It seems plausible that the vowels preceding [m] in these words were pronounced with some amount of phonetic nasalization, but this kind of "nasal vowel" wouldn't have been phonologically distinct from a regular Latin vowel phoneme: the presence of nasalization here would be entirely predictable from the phonological context (as is the case for vowel nasalization in present-day English, which isn't normally marked in phonetic transcriptions). I don't know of any actual evidence that these vowels were nasalized.
The (possible) presence of nasal vowels in word-final position, or before voiceless fricatives, is notable because we have evidence that the nasal consonants that originally conditioned the nasality of the vowels may have been lost in these two contexts, with "compensatory" lengthening of the vowel. We have clear evidence of the lengthening of vowels before NF and NS, and fairly clear evidence of the possible loss of N before F or S, and of M in word-final position before a vowel. My understanding is that the existence of distinctively nasal long vowels in Latin (as opposed to non-nasal long vowels, or vowel + nasal consonant sequences) is mostly an inference, not something that we have clear evidence for (and so, as Alex B.'s answer mentions, it is a bit controversial).
*The pronunciation of M inside compounds might be a bit unclear in some cases
The pronunciation of certain compound words where the first element ends in m and the second element starts with a vowel, e.g. circumeo, is apparently doubtful. Andras Cser's "Aspects of the Phonology and
Morphology of Classical Latin" (2016) has a section on circum- (18.104.22.168.). In some forms of circumeo, it was common to not write the letter M (e.g. circuit), which could be interpreted as an indication that nasality was totally lost in these forms.
Place assimilation is assumed to have turned originally word-final M into [m] before [p b], [n] before [t d], and [ŋ] before [k g]. For some words, we have evidence for these changes in the form of a spelling with N: thus eam + -dem > eandem.
This kind of place assimilation is thought to have applied, even when unwritten, to the M that occurs as part of inflectional suffixes. So the form "uirumque", with the enclitic -que, probably would have been pronounced without an [m] sound as something like [wɪˈrʊŋkwɛ].