Korea had slavery until 1894. It was abolished in 3 phases: 1801, 1886, and 1894.

Records are spotty and it is hard to get exact numbers or situations. The majority of slaves were prisoners of war, criminals, and their descendants. Korean slavery had many levels and groups. Privately owned slaves and government slaves, in slaves and out slaves, etc. The line between slave and tenant farmer was almost invisible with some slaves working directly for the master and some simply paying tribute.

Specifically, 1765, slavery was legal in Korea but on the decline as most wealthy folks found it easier to take rent from tenants than to own slaves.

Micahel Seth's A History of Korea has a brief bit on the time period you're asking about with more details on the different levels and divisions of slavery.