Why are Mīmāṃsā authors seemingly not at all interested in the topic of liberation (mokṣa)? The problem is closely linked with that of the relation between Vedānta and Mīmāṃsā (since the former primarily deals with the self, its status in liberation, its proposed identity with the brahman). Asko Parpola in two insightful studies proposed that the Mimamsasutra was originally a single work, only later segmented into Mīmāṃsāsūtra and Brahmasūtra. Until that point, it has been commented upon as a unitary work. Hence, the two schools later known as Pūrva Mīmāṃsā and Uttara Mīmāṃsā (i.e., Vedānta) derive their names from the two segments Pūrva-Mīmāṃsāsūtra and Uttara-Mīmāṃsāsūtra (where pūrva means prior and uttara subsequent).
Bronkhorst, in his long essay at the beginning of the Mīmāṃsā and Vedānta volume he edited in 2007 (and including the proceedings of the Mīmāṃsā and Vedānta panel in the 12th WSC), contends that this thesis (formerly upheld also by Jacobi) does not hold. In fact, if Mimamsa and Vedanta had ever been a single school, then one would expect (Pūrva)-Mīmāṃsākas to be keen to speculate also about Vedāntic subjects, such as ātman, brahman, mokṣa. Since this is not the case, Mīmāṃsā and Vedānta were never a single śāstra.
Bronkhorst employs many evidences and, in fact, the Brahmasūtra is overtly later than the Mīmāṃsāsūtra (hence, Parpola and others had to postulate that the actual Brahmasūtra is not identical with the Uttara-Mīmāṃsāsūtra, which makes their thesis cumbersome).
I wonder, however, whether the former "unity" of Vedanta and Mīmāṃsā should not rather be read as an alliance, just like in the case of Nyāya and Vaiśeṣika. Vedānta would accept all Mīmāṃsā tenets and Mīmāṃsā would refrain from considering proper Vedanta subjects. The two schools would form a unity insofar as they are complementary. Bronkhorst himself states that "Vedāntic Mīmāṃsā in a certain way recognises ritual Mīmāṃsā" (p. 25).
However, unluckily enough, Bronkhorst's learned essay does not deal with this option.