FYI, the link to the “latest DirectX runtime” (http://www.microsoft.com/en-us/download/details.aspx?id=35) on the MonoGame Download site is broken. The link referred to the “DirectX end-user runtime web installer”. The only alternative link that I can find is
DirectX End-User Runtimes (June 2010): https://www.microsoft.com/en-us/download/details.aspx?id=8109
Is this the correct link or are there alternative DirectX End-User Runtime downloads somewhere out there?