plotting - FrameTicks and Ticks on Axes in Same Plot

I have a plot where I would like ticks shown on both the axes and the frame, with them labeled separately. I have custom labels for the frame and want the horizontal axis labeled with ticks automatically. Despite setting both the Ticks and the Frame properties, I cannot get the ticks to show up on the axes. Is there a way to do this without drawing the ticks manually or something like that? My example is shown below, I am able to get automatic ticks on the top of the frame, but these are not labeled either.

Plot[xt[t], {t, 0, .5*10^-3}, 
  Ticks -> Automatic, 
  FrameLabel -> {{"x [m]", None}, {"t", None}},
  Frame -> True,
  FrameTicks -> {{Automatic, None}, {{{0, "t'"}, {.0005, "t'+5 ms"}}, Automatic}}]

Plot with no axes ticks

Answer

As noticed in this topic it is impossible an could be confusing. The solution is as usual, Overlay :)

With[{opt = Sequence[ImagePadding -> {{65, 25}, {40, 15}}, BaseStyle -> {Bold, 15}]},

 Overlay@{

   Plot[Sin[t], {t, 0, 2 Pi}, FrameLabel -> {{"x [m]", ""}, {"t", ""}}, Frame -> True, 
    FrameTicks -> {{Automatic, None}, {{{0, "t'"}, {2 Pi, "t'+5 ms"}}, Automatic}}, 
    Axes -> False, opt],

   Plot[Sin[t], {t, 0, 2 Pi}, Axes -> {True, False}, PlotStyle -> None, opt]

 }]

enter image description here

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