Inverse CDF sampling for a statistically 3-dimensional vector

For a 3-dimensional vector random variable, whose components are statistically dependent, I want to generate i.i.d. samples for the following joint PDF in 3-dimensions 𝑓𝑋𝑌𝑍 ( 𝑥, 𝑦, 𝑧 ) = 𝑘(𝑥 + 𝑦 + 𝑧) where k is the normalization constant supported on the unit cube

0 ≤ 𝑥, 𝑦, 𝑧 ≤ 1