In plain words
Even while always performing all actions, one who takes refuge in Me attains, by My grace, the eternal and imperishable state.
Word for word
Even always doing all actions, one whose refuge is Me attains by My grace the eternal, imperishable state.
The commentators
Bhagavadgītābhāṣyam
स्वकर्मणा भगवतः अभ्यर्चनभक्तियोगस्य सिद्धिप्राप्तिः फलं ज्ञाननिष्ठायोग्यता, यन्निमित्ता ज्ञाननिष्ठा मोक्षफलावसाना । सः भगवद्भक्तियोगः अधुना स्तूयते शास्त्रार्थोपासंहारप्रकरणे शास्त्रार्थनिश्चयदार्ढ्याय —
सर्वकर्माण्यपि प्रतिषिद्धान्यपि सदा कुर्वाणः अनुतिष्ठन् मद्व्यपाश्रयः अहं वासुदेवः ईश्वरः व्यपाश्रयो व्यपाश्रयणं यस्य सः मद्व्यपाश्रयः मय्यर्पितसर्वभावः इत्यर्थः । सोऽपि मत्प्रसादात् मम ईश्वरस्य प्रसादात् अवाप्नोति शाश्वतं नित्यं वैष्णवं पदम् अव्ययम् ॥ ५६ ॥
In plain words
Doing your own work as worship of the Lord — that is bhakti-yoga, and what it yields is siddhi: you become fit to stand firm in knowledge. Given that fitness, jñāna-niṣṭhā follows, and it ends in mokṣa and nowhere else. So now, in the closing section where the meaning of the whole teaching is gathered up, that yoga of devotion to the Lord is praised — to set the sense of the scripture firmly beyond doubt —
Doing — that is, actually carrying out — all actions, always, even the ones scripture forbids: madvyapāśrayaḥ. I, Vāsudeva, the Lord, am the refuge; the man whose taking of refuge is in Me is the one the verse calls madvyapāśrayaḥ. His whole inner life has been laid down in Me — that is what the word means. Even he, by My grace, by the grace of Me who am the Lord, reaches the lasting — the eternal — state that is Viṣṇu's own, and it does not wear away.
Close to the Sanskrit
The fruit of the yoga of devotion which is the worship of the Lord through one's own work is the attainment of perfection — namely, fitness for steadfastness in knowledge; occasioned by which, steadfastness in knowledge terminates in liberation as its fruit. That yoga of devotion to the Lord is now praised, in the section that concludes the meaning of the scripture, for firmness in the ascertainment of the scripture's meaning —
Doing (kurvāṇaḥ), that is, performing (anutiṣṭhan), always all actions, even the prohibited ones — madvyapāśrayaḥ: I, Vāsudeva, the Lord, am the vyapāśraya, the resort; he whose taking-of-refuge (vyapāśrayaṇa) is in that, he is madvyapāśrayaḥ. One whose whole being is offered in Me — that is the meaning. He too, by My grace, that is, by the grace of Me, the Lord, attains the śāśvata, the eternal, Vaiṣṇava state, the imperishable.