Cuenca studied Art History at the Universidad Iberoamericana in Mexico City. From 2011 to 2014 she was Director of the Tamayo Museum, INBA. She also served as the Subdirector for visual arts at the Tijuana Cultural Center, CECUT, from 2006-2009. From 1982-1989, she worked in the Department of Investigation at the San Carlos Museum, INBA. From 1994 to 1997, she served as Cultural and Executive Director of the Mexican Cultural Institute in San Diego CA. She has participated in the different versions of inSite, public art project in Tijuana/San Diego as Coordinator for Mexico in inSite94 and Executive Co-director in inSite 97, inSite2000 and inSite05. Currently, she is Executive Director of inSite/ Casa Gallina for Mexico. Cuenca has participated in diverse patronages and councils of non-profit organisations including the Children’s Museum of San Diego (1997-2001), the Athaeneum Music and Arts Library in La Jolla (2002-2014) and the Patronato de Arte Contemporáneo (Contemporary Art Patronage), PAC, in Mexico City.