By the Remainder Theorem, when $P(x)$ is divided by $x + 1$, the remainder is $P(-1)$.
We are given that the remainder is 6, so $P(-1) = 6$.
$P(-1) = (-1)^3 + 3(-1)^2 - 5a(-1) - 6 = -1 + 3 + 5a - 6 = 5a - 4$.
Therefore, $5a - 4 = 6$, which gives $5a = 10$, so $a =
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