With your AP ICET rank of 5861, you fall within the 3001 to 10000 rank range, which generally aligns with Tier D level colleges for free seat admissions in Andhra Pradesh. Based on previous cutoffs and trends, here are ten MBA colleges where you have a good chance of getting a free seat during the July counselling:

Andhra University College of Arts and Commerce Visakhapatnam
Sri Krishnadevaraya University Anantapur
JNTU School of Management Studies Self Finance Kakinada
Nimra College of Engineering and Technology Jupudi
SVU College of Commerce Sri Venkateswara University
JNTU College of Engineering Self Finance Vizianagaram
SD College of Information Technology Tanuku
Aditya Degree College for Women Rajahmundry
RVR and JC College of Engineering Guntur
Rajiv Gandhi Degree and PG College Rajahmundry