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"Silent" shutter on the 1DX is kind of old school (i.e fiction). In 'silent' mode, you push the shutter to take the photo (i.e. auto-aperture stops down, mirror flips up, shutter fires). The mirror doesn't go back down, until you release the shutter button. That way, it reduces the loud "click, clack", to "click, ... ... clack".
"Silent", it is not. OTOH, silent shutter on the 6D is way quiet. Somewhere in between the X100 and X-Pro 1 (the X100 is silent, the X-Pro 1 is quiet).
Long story short, the 1DX is not a quiet camera. OTOH, it's an AF and high-fps monster.