Advaita or non-dualism is in agreement with Mimamsa up to a point. It accepts Vedic karma as well as the six pramanas (perceptions or sources of knowledge) defined by Kumarilabhatta. Sankara's non-dualism, Ramanuja's qualified non-dualism, and Madhva's dualism are all Vedantic doctrines and all three are not against Vedic rituals. While non-dualism accepts all the six pramanas of Mimamsa, qualified non-dualism accepts only three- pratyaksa, anumana and the Vedas. I will explain these terms when I deal with Nyaya.
The three leading Vedantic teachers (Sankara, Ramanuja and Madhva), do not completely reject Mimamsa, but the paths they have cut out go beyond the mimamsic view: devotion in the case of Visistadvaita and Dvaita and jnana in the case of Advaita.
Mimamsa is called karmamarga since it teaches that karma is all. But karma here does not have the same meaning as in Vedanta which speaks of the three paths- karma, bhakti and jnana. In Vedanta karma is not performed for the sake of karma and is not an end in itself, but consecrated to Isvara without any expectation of reward. This is also karmamarga or karmayoga. It is this view of karma that the Lord expounds in the Gita. In the karmamarga of mimamsakas there is no bhakti. But, all the same, the Vedic rituals create well-being in the world, lead to a disciplined and harmonious social life and bring inner purity to the performer. Mimamsa holds karma to be a goal in itself; Vedanta regards it as a means to a higher end.
For a general background, please see here